Armstrong has been linked with moves away from Celtic in the summer transfer window, with clubs in the Premier League claimed to be interested.
According to The Scottish Sun, Southampton and Brighton and Hove Albion want the 25-year-old midfielder, while The Birmingham Mail has credited West Bromwich Albion with interest in the former Dundee United star.
Campbell worked with the Scotland international midfielder at Dundee United, and he has suggested that the talented player should remain at Celtic Park for the 2017-18 campaign.
The former Dundee United youth supremo, who The Sunday Post has described as Armstrong’s former mentor, has also stated that Celtic star is good enough to play in Spain, Germany or Italy.
“Stuart has the technique and the ability to go abroad,” Campbell told The Sunday Post. “But he also has the brains to cope with a move to Germany, Spain or Italy.
“In actual fact, I’d probably rather see him do that. But, equally, I’d love to see him one day in the Premier League.
“Because of where it all started, it’s brilliant to have watched him progress to where he is now. It’s even more exciting to think about where he could be this time next year.”
"I would think that would be ideal,” added Campbell regarding whether Armstrong should stay at Celtic next season. “He has had a brilliant eight months but he’s a very level-headed young man.
“He absolutely loves it at Celtic, playing under Brendan Rodgers and also working with Chris Davies.”
As reported by The Birmingham Mail, the 25-year-old midfielder scored 15 goals in 31 Scottish Premiership games for the Hoops last season.